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Stephan Henzler Mixed-Signal-Electronics 2011/12

Mixed-Signal-Electronics

PD Dr.-Ing. Stephan Henzler

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Lecturer CV

Stephan Henzler received the Dipl.-Ing. degree in

electrical engineering in 2002, the Dr.-Ing. degree in 2006,

and the habilitation1 degree in 2010 from the Technische

Universität München (TUM), Germany. From 2002 to

2005, he was with the Institute for Technical Electronics,

Technische Universität München, where he worked on

low-power digital integrated circuit design and leakage

reduction techniques. For his dissertation on power

management and leakage reduction techniques he

received the Rhode-und-Schwarz outstanding thesis

award 2007. In 2005, he joined the Advanced Systems

and Circuits Department of Infineon Technologies AG,

Munich, where he worked on high-speed/high-

performance digital integrated circuits, variability in deep-

submicron CMOS technologies, and mixed-signal circuit

design in nanometer CMOS technologies, especially time-

to-digital converters. In 2010 he joined the wireless mixed-

signal department of Infineon where he works on mixed-

signal system and circuit design. Since February 2011 he

carries on the same responsibilities within Intel.

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[email protected]

mailto:[email protected]


Simplicity is the Ultimate Sophistication Leonardo Da Vinci

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Stephan‟s ambition for this course …

But don‟t misunderstand,

this does not mean that you

don‟t have to exercise!


Course and Online Material Lecture notes

available in the Fachschaft EI (TUM), handout (GIST TUM Asia)

Online material comprising

– annotated slides

– video stream of past lectures (GIST TUM Asia)

4 www.lte.ei.tum.de/homes/henzler


Administratives

Lecture: Stephan Henzler

[email protected]

office hours: online consultation

Tutorial: Cenk Yilmaz

[email protected]

office hours online & by arrangement

Exam: in written form,

preliminary date February, 17th 2012

Credits: 4.5 ECTS credits (TUM)

Language: english

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“Today everything is digital –

Why do we need Mixed-Signal-Electronics?”

Digital System, e.g.

- digital communication

(DSL, GSM, …, LTE)

- computer equipment

- multimedia

(DVD, mp3, camera… )

- control application

(e.g. automotive)

discrete sequence of

numbers from a discrete set

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The Macroscopic World is Purely Analog





- multimedia



(e.g. automotive)



Our environment is always analog …

You just have to investigate the system in-depth!

light

sound waves

mechanical force

electromagnetic

field

temperature sense organs

time

continuous time

and values

even „digital‟

signals on a

transmission

channel

motion/acceleration

sensors/

actuators

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The Macroscopic World is Purely Analog

The mixed-signal shell is a bridge between

– the analog environment and the digital signal processing

– the physical representation (voltage/current) and a mathematical abstraction

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- multimedia



(e.g. automotive)



light

sound waves

mechanical force

electromagnetic

field

temperature sense organs

time

even „digital‟

signals on a

transmission

channel

motion/acceleration

sensors/

actuators

ADC

DAC


Topics of MSE Course

Structure of mixed signal systems and mathematical

representation of discrete time signals.

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ADC

discrete time (step function)

continuous states

discrete time

discrete states

digital discrete time (step function)

discrete values (states)



Structure of mixed signal systems and mathematical

representation of discrete time signals.

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Sample & hold circuits

Switched-capacitor circuits

Data converter fundamentals (ADC, DAC)

converter parameters and characteristics

Nyquist rate D/A Converters

Nyquist rate A/D Converters

Oversampling Converters

Outlook: More mixed signal building blocks

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Recommended Literature

Relevant chapters: Chapter 7:

Comparators.

Chapter 8:

Sample-and-Holds

Chapter 9:

Discrete Time Signals

Chapter 10:

Switched Capacitor Circuits

Chapter 11:

Data Converter Fundamentals

Chapter 12:

Nyquist-Rate D/A Converters

Chapter 13:

Nyquist-Rate A/D Converters

Chapter 14:

Oversampling Converters

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Additional Literature & References

Razavi. Principles of Data Conversion System Design.

Wiley, 1994.

Allen, Holberg. CMOS Analog Circuit Design. Oxford, 2010.

Baker, Li, Boyce. CMOS Circuit Desig, Layout, Simulation.

Wiley, 1997.

Gregorian, Temes. Analog MOS Integrated Circuits for

Signal Processing. Wiley 1986.

Oppenheim. Time Discrete Signal Processing. Oldenbourg

Norsworthy, Schreier, Temes. Delta-Sigma Data

Converters. IEEE Press, 1997.

Schreier, Temes. Understanding Delta Sigma Data

Converters. IEEE Press 2005.

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Constraints of Mixed Signal Circuits in SoC

PROS CONS • Cheap implementation of complex

signal processing tasks

• System-on-chip (SOC)

Small pcb footprint

• Fast time reference/clock

• Digitally assisted analog

• All advantages of digital

systems, e.g. robustness, noise

immunity, data storage,

reconfigurability, efficient highly

automated design and test

• Need to build analog circuits in

digital process, i.e.

• Devices optimized for high

switching speed not for analog,

(e.g. small gm/gds)

• Transistors with high field

and short channel effects

µ(VG), Vth(W,L,VDS,VBS), Igate, IDB

• Signal contamination due to digital

switching noise, e.g. cross talk,

supply noise substrate coupling

• several 100mA digital currents

• V analog signals

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Basics of Mixed-Signal Electronics

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Chapter 1


Generic Structure of Mixed-Signal Systems

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System Perspective

Circuit Perspective


Representation of Discrete Time Signals and

Spectral Transformation

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xs(t) = xc(t)X

n

±(t¡ nT)

=X

n

x(nT)±(t¡ nT)

=X

n

x[n]±(t¡ nT)




Fourier Transformation

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X(!) =

+1Z

¡1x(t)e¡j!tdt

x(t) =1

2¼

+1Z

¡1X(!)ej!td!

X(s) =

+1Z

¡1x(t)e¡stdt

generalization

s = j

Laplace Transformation


Insertion of sampled signal in Fourier formula:

Normalization of frequency to sampling frequency:

X(!) =

+1Z

¡1

X

n

x(nT)±(t¡ nT)e¡j!tdt

=X

n

x(nT)

+1Z

¡1e¡j!t±(t¡ nT)dt

=X

n

x(nT)e¡j!nT

Spectral Transformation of Discrete Time Signal

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X() =X

n

x[n]e¡jn X(z) =X

n

x[n]z¡ngeneralization

z = ej= ej!T

z-Transformation FT of discrete sequence

FT of sampled signal

= !T =2¼f

fs




Meaning of frequency: oscillations per second.

What is meaning of normalized frequency Ω?

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Ω = angular change from sample to sample



Spectral Transformation Spectrum of a sampled signal:

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Sampling means multiplication

of continuous time signal with

pulse train

In frequency domain this translates

into convolution of signal spectrum

with spectrum of pulse train.

This is simply a copy and shift of

the spectrum to multiples of the

sampling frequency

s(t) =X

n

±(t¡ nT) $

xs(t) = xc(t) ¢ s(t) $

S(!) =2¼

T

X

k

±(! ¡ k!s) !s =2¼

T

Xs(!) =1

2¼Xc(!) ¤ S(!)

=1

TXc(!) ¤

X

k

±(! ¡ k!s)

=1

T

X

k

Xc(! ¡ k!s)




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Aliasing occurs if mirror spectra overlap


Aliasing in the Frequency Domain

23

t

t

t

t

t

t

low-pass filtering low-pass

low-pass

low-pass

theoretical case as brick wall

filter would be required


Sampling and Aliasing 1

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0 5 10 15

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

samples

am

plitu

de

fsampling = 1 f signal,1 = 0.22



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0 5 10 15

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

samples

am

plitu

de

fsampling = 1 f signal,2 = 0.22 + fsampling


0 5 10 15

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

samples

am

plitu

de


Only with the Nyquist criterion it is assured that the samples

represent the signal unambiguously

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Remember: All realizable signals have

– finite slope (dx/dt)

– finite pulse width, i.e. finite bandwidth

– finite value

Practical Sampling: Sample & Hold

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t

t

t

ideal sampling

step function

alternative solution


Remember: All realizable signals have

– finite slope

– finite pulse width

– finite bandwidth

– finite value

Hence sampling means always SAMPLE & HOLD

Practical Sampling: Sample & Hold

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Sampling with Finite Pulse Width

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xsh(t) = xs(t) ¤ h(t)

=

1X

n=¡1xc[n]

1

¿[¾(t¡ nT)¡ ¾(t¡ nT ¡ ¿)]

xsh(!) =1

¿

+1Z

¡1

1X

n=¡1xc[n] [¾(t¡ nT)¡ ¾(t¡ nT ¡ ¿)] e¡j!t dt

=1

¿

1X

n=¡1xc[n]

nT+¿Z

nT

e¡j!t dt

= ¡ 1

j!¿

1X

n=¡1xc[n]

he¡j!t

inT+¿

nT

t

(t)


Sampling with Finite Pulse Width

Distortion of base band and damping of mirror spectra

– visible in DAC

– not visible in ADC

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Xsh(!) = ¡ 1

j!¿

1X

n=¡1xc[n]

³e¡j!nTe¡j!¿ ¡ e¡j!nT

´

=

1X

n=¡1xc[n]e

¡j!nT 1

j!¿

³1¡ e¡j!¿

´

= Xs(!)e¡12j!¿ e

j12!¿ ¡ e¡j

12!¿

2j12!¿

= Xs(!)e¡j1

2!¿

sin³12!¿

´

12!¿

ideal sampling XS() impact of hold




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Relation Between s- and z-Plain

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X(!) =

+1Z

¡1x(t)e¡j!tdt

X(s) =

+1Z

¡1x(t)e¡stdt X(z) =

1X

n=¡1x[n]z¡n

j

s

Re(z)

Im(z)

z z = ej!T

Fourier Transformation:

LaPlace Transformation: z-Transformation:

1X

n=¡1x(nT)e¡j!nT

generalization normalization

&

generalization

discrete

signals


Downsampling

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Additional information: If there is noise betwen the repeated signal spectra, or if the Nyquist criterion cannot be guaranteed for the

downsampled signal an additional filtering is required (low pass). However, it is sufficient to compute one out of L samples.


Downsampling II

Down-sampling requires, that there is no signal energy in

between baseband and mirror spectra (e.g. noise)

In general this is not the case, so down-sampling may cause

aliasing

To avoid aliasing a low pass filter is required in front of down-

sampling block Decimation Filter (Decimator)

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Upsampling

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Additional information: Fractional sample rate conversion is up-sampling combined with down-sampling. Low-pass filters

may be shared. Compute only what is necessary!

imaging


Upsampling II

Zero padding results in higher sampling rate

However, this does not mean that mirror spectra occur only

at multiples of the sampling frequency

Imaging, i.e. replica in between 0..2

Low pass filter removes images

– Result in frequency domain: Replica only at k x fs

– Result in time domain: Zeros move on real signal curve

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Fractional Sample Rate Conversion

Purpose: Change sample rate by a non-integer factor L/M

Two possibilities:

– Up-sampling by L, down-sampling by M

– Down-sampling by M, than up-sampling by L

The order of up- and down-sampling may be exchanged

without any change in the input/output behavior if the

decimation factor M and the interpolation factor L are

relatively prime.

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